It comes following a national report on Monday night which stated that the club had held talks with other English Football League clubs about a potential move away from Oakwell amid a furious row over the purchase of the ground.
Barnsley Metropolitan Borough Council own fifty per cent of Oakwell with the Cryne family owning the other half.
The report in the Daily Mail about Barnsley potentially relocating away from Oakwell prompted the leader of Barnsley Council to voice his shock and dismay at the possible development, while pledging that the authority would do all they can to make sure that professional football remains in the town.
The report claimed that a source close to the club said that the blocking of a previous attempt to buy half of the stadium from the authority left the Reds' majority shareholders ' 'discouraged and immediately seeking alternative arrangements'.
Any move from Oakwell would need permission from the EFL board.
Issuing their own response to developments, a statement issued on behalf of the Cryne Family, who retain a twenty per cent club shareholding - having sold eighty per cent of the club to the Hong-Kong based BFC Investment Company in December 2017 - read: "The Cryne Family would like to clarify that contrary to recent speculation they are fully committed to the agreement to sell their 50 per cent stake in Oakwell Stadium to BFC Investment Company, the Hong Kong consortium that owns Barnsley Football Club.
"BFC Investment Company exercised an option in January 2020 to buy the Cryne family’s 50 per cent share in the company which owns Oakwell Stadium.
"The other 50 per cent is owned by Barnsley Metropolitan Borough Council. Since exercising the option, BFC Investment Company has raised a number of concerns in relation to that option. The Cryne Family has responded in full to these concerns, on which they have previously taken Counsel’s opinion from two leading QCs.
"The Cryne Family remain committed supporters of the Club and its future at Oakwell Stadium, the Club’s home where it has played its football for the past 133 years, and want no more than to resolve this issue in line with the agreement made when BFC Investment Company bought the Club."
In their own statement sent to The Yorkshire Post which responded to the report that Barnsley could relocate away from Oakwell, Cllr Sir Steve Houghton CBE, leader of Barnsley Council, said: "We're shocked and dismayed at the comments regarding the potential relocation of Barnsley Football Club.
“Relationships between the council and Barnsley Football Club have always been excellent. There are no disputes between the club and the council. The council has not declined to transfer the land as there have been no negotiations between the two parties on this matter.
"For the last 133 years, Barnsley Football Club has been a significant part of our borough, and we'll do all we can to make sure professional football is maintained in Barnsley."